a)
[tex]sin^2\alpha + cos^2\alpha = 1\\cos^2\alpha = 1 - sin^2\alpha\\\frac{cos^2\alpha-1}{sin\alpha} = \frac{1-sin^2\alpha - 1}{sin\alpha} = \frac{-sin^2\alpha}{sin\alpha} = -sin\alpha[/tex]
b)
[tex]tg\alpha = \frac{sin\alpha}{cos\alpha}\\\\sin^2\alpha + cos^2\alpha = 1\\cos^2\alpha = 1 - sin^2\alpha\\\\sin^2\alpha=1-cos^2\alpha\\\frac{(1-sin^2\alpha)-tg\alpha}{cos\alpha} = \frac{cos^2\alpha-\frac{sin\alpha}{cos\alpha}}{cos\alpha}=\frac{cos^2\alpha-\frac{sin\alpha cos\alpha}{cos^2\alpha}}{cos\alpha} = \frac{cos\alpha(cos\alpha-\frac{sin\alpha}{cos^2\alpha})}{cos\alpha} = cos\alpha - \frac{sin\alpha}{cos^2\alpha}[/tex]
